SOLUTION: I need help solving this linear equation in three variables 5y -7z = 14 2x + y + 4z = 10 2x + 6y - 3z = 30 please help me solve this equation.\ thanks megan

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Question 153589: I need help solving this linear equation in three variables
5y -7z = 14
2x + y + 4z = 10
2x + 6y - 3z = 30
please help me solve this equation.\
thanks
megan

Found 2 solutions by Edwin McCravy, stanbon:
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
I need help solving this linear equation in three variables
5y -7z = 14
2x + y + 4z = 10
2x + 6y - 3z = 30
please help me solve this equation.
thanks
megan

There is no solution.  This is what is called an inconsistent
system.

There are many methods to solve a system of three equations
in three unknowns. If you will re-post telling which method
you are studying, then we can use that method and show how 
you can tell that there is no solution.

Edwin


Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
0x + 5y -7z = 14
2x + y + 4z = 10
2x + 6y - 3z = 30
-------------------------
Switch line 1 and line 2 to get:
-------------------------
2x + y + 4z = 10
0x + 5y -7z = 14
2x + 6y - 3z = 30
-------------------------
Subtract line 1 from line 3:
2x + y + 4z = 10
0x + 5y -7z = 14
0x + 5y -7z = 20
-------------------------
2x + y + 4z = 10
0x + 5y -7z = 14
0x + 0y -0z = 6
------------------------
The 3rd line is a contradiction and indicates there is no
solution to the system of three equations.
===========================
Cheers,
Stan H.


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